The orbit of Earth around the Sun is elliptical, and we are given the following:

• The semi-major axis $a = 92.9 \, \text{million miles}$.
• The eccentricity $e = 0.017$.

To find the closest distance (perihelion) and the farthest distance (aphelion) between the Earth and the Sun, we can use the following formulas for an elliptical orbit:

• Perihelion (closest distance): $r_{\text{perihelion}} = a(1 - e)$
• Aphelion (farthest distance): $r_{\text{aphelion}} = a(1 + e)$

Calculations:

1. Perihelion: $r_{\text{perihelion}} = 92.9 \times (1 - 0.017) = 92.9 \times 0.983 = 91.3017 \, \text{million miles}$

2. Aphelion: $r_{\text{aphelion}} = 92.9 \times (1 + 0.017) = 92.9 \times 1.017 = 94.4983 \, \text{million miles}$

Final results:

• Closest distance (perihelion): 91.3 million miles.
• Farthest distance (aphelion): 94.5 million miles.

Would you like more details or have any further questions?

Here are 5 questions you could explore next:

1. What is the definition of eccentricity in an elliptical orbit?
2. How does the eccentricity of Earth's orbit compare to other planets?
3. How do Kepler’s laws of planetary motion relate to this problem?
4. How does the distance between the Earth and Sun affect the seasons?
5. What would happen to Earth's orbit if its eccentricity increased?

Tip: The Earth's orbit is nearly circular, but the small eccentricity still plays a role in seasonal temperature variations.